Every single atom which goes into a chemical reaction MUST come out the other side, even if atoms are grouped differently than when they go in.

No matter HOW the atoms are arranged, every single “atom” that went in MUST come out the other side. In this case, 3 red, 2 yellow and 5 blue “atoms” MUST come out the other side. That is the first condition you must meet to have a balanced equation.

“Conservation” means that nothing gets lost, nothing gets created out of thin air. “Mass” refers to the amount of matter. There is no such thing as “losing atoms” in a chemical reaction. Nor can atoms suddenly appear when they weren’t there in the first place.

Coefficients and Subscripts:

Know how to interpret the two kinds of numbers found in chemical equations.

Large numbers in red are called “coefficients,” because they “appear with” the formulas and act as multipliers. (“Co” means “with” and “efficient” comes from a Latin word meaning “to accomplish.”

small numbers in blue are called “subscripts,”because they are written below the line. (“Script” for “writing” and “sub” for “below.”)

Introducing Color Code Formulas

For now we’ll use colored circles as our “atoms” and the first letters of their color names as our “chemical symbols.” For example:

Subscripts Tell How Many Atoms of Each Kind

The subscript tells us how many atoms of each kind exist in any formula.
The subscript is ALWAYS written AFTER the symbol of the atom to which it refers.

When an atom appears only ONCE in a formula, we don’t write the subscript, because it’s not needed.

Combining Two Different “Color” Atoms

What happens when we combine two or more different atoms together? How do we write the formulas then? We’ll write the formula for a molecule made of one atom of blue and one atom of white.

Since we are only working with colors and not actual element symbols, it does not matter whether we write “B” first or “W” first.

Notice also that whichever formula we choose, the formula stays the same, regardless of the molecule’s orientation in space.

Now we will write the formula for 1 atom of blue and 2 atoms of white.

In most cases when 1 atom of one kind and 2 of another are put together, the single atom will be the central atom of the molecule, as shown in the first four examples in the box above.

The last two examples, in which blue is NOT the central atom, were added to show that the formula describing how many atoms there are of each kind is the same, regardless of how the atoms are connected or how they are oriented in space.

Now we will combine 1 atom of blue and 3 atoms of white.

In this case, the atoms will almost always connect with each other as shown in the first example, although the second example is still possible.

Main point: the subscript written after a symbol tells how many atoms of that kind there are in the formula. It does not give any information about HOW the atoms are connected to each other.

Just a side note: There ARE rules for writing chemical formulas, such as which atom symbol is written first, and the formulas CAN show something about connectivity, especially in the case of organic molecules (molecules which exist in living creatures)

Our goal here is to understand enough about formulas to balance a chemical equation, so we will ignore the rules of writing sophisticated chemical formulas for now.

Later, when we want information about how to write chemical formulas, there will be a link for you to go to a different web page.

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Here is one more set of examples showing how the subscript gives us information about the number of each kind of atom in a formula. Study the following examples and make sure you understand how the formulas below relate to the pictures of the molecules above them.

Coefficients are Multipliers

Let’s see how coefficients are used in chemical equations.

A coefficient is a multiplier. Here are some examples.

The coefficient multiplies, and applies to, the ENTIRE FORMULA written after it, not just the first letter.

When you have the balanced equation, you can multiply the coefficient by the subscript for each atom in the formula to find out how many total atoms you have of each kind.

(Remember, when there is only one atom of a kind in the formula there is no subscript written, so we use “1” as the subscript multiplier.)

Do not make this mistake.

This is just one example of a mistake many students make. The number of atoms of each kind is the same in both cases, but these two molecules are VERY different from each other. Do not EVER make the mistake of writing “3 BW2” as “B3W6” or anything like that.

Balancing Equations.

OK. Now that you have the basics down, let’s start actually balancing equations. Just remember that once all the formulas in the initial equation are correct, the ONLY thing you can do to balance an equation is to add groups by changing the coefficients. Once the formulas are correct, you must NOT change the subscripts.

Example 1:

Look at this simple equation. Immediately underneath it are drawings of the molecules these formulas represent. Our task is to find the lowest number of groups of each formula such that all the atoms are accounted for and balanced on both sides of the equation. The “reactants side” of the equation is anything written BEFORE the arrow. The “products side” of the equation is anything written AFTER the arrow.

….

It can be seen by inspection that there are 2 red atoms on the left and only 1 redatom on the right. Thus, this equation is NOT balanced.

In order to balance the quation, we need at least 1 more red atom on the right side, but we cannot add JUST 1 red atom. Rather, we must add an entire GROUP of atoms which contains our red atom of interest. It’s somewhat like buying a box of crayons. In order to get one crayon of a certain color, you must buy the entire box, because they just don’t come one crayon at a time.

We have to add at least one red atom to the right side, but in order to do that, we have to add one entire group, so let’s do that and see what we get.

Adding the group balances our red atoms, giving us 2 red atoms on each side. However, now the whites are unbalanced. We have 2 white atoms on the left side of the arrow but 4 on the right side. What should we do? Of course, “add a group.”

Now if we look at the equation, we see that there are the same number of each kind of atom on both sides of the equation. So this equation is now balanced. All that is left for us to do is write down the coefficients.

Remember, you cannot represent “2 W2” as “W4.”

Nor can you represent “2 RW2” as “R2W4.”

So the balanced equation is:

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Again, we drew the molecules represented by the formulas in the equation. First let’s balance the blue atoms. How many blue atoms are there on the left, or “reactants side” of the equation? How many on the right, or “products side”? In order to get one more atom of blue on the right side, what do we need to add? Yes, we need to add an entire group. So let’s do that.

See that we have also added the red coefficient, 2, in front of the formula, BW3 , to reflect the addition. This now balances our blue atoms, but the whites are still unbalanced. How many white atoms do we have on the right side of the equation? [Answer: 6] And how do we get 6 atoms of white on the left hand side? Yes, by adding groups. What is the total number of groups we need on the left to balance the 6 whites on the right?

So now we have another correctly balanced equation.

Example 3:

With this equation, first let’s look at the yellow atoms. There is 1 yellow on the left, but 2 yellows on the right. What do we do?

OK. This balances our yellows, but our reds are still unbalanced. What do we do next?

A word of caution here. Many students at this point make a BIG mistake! They actually take atoms AWAY from Y2R3 and change the formula to Y2R2, as shown below! Don’t you do this!

The ONLY thing we can EVER do in balancing equations, once the formulas are correct, is to ADD groups.

So what groups should we add? If we add one group of R2, as shown below, this still doesn’t balance the reds.

Can you guess the secret? The secret is to find the least common multiple, (yes, an application of math!) between the original 2 reds on the left side and the 3 reds on the right. What is the least common multiple of 2 and 3? [Answer: 6] How do we get 6 reds on both sides?

Yes, “3 groups of 2” and “2 groups of 3.”

But now the yellows are unbalanced again. What do we do next? Remember, 4 Y does NOT equal Y4.

We change the coefficient in front of “Y” to 4.

So the final balanced equation is:

One last word: When balancing equations, you ALWAYS want the lowest possible numbers. For example, the above equation may also be written as:

All of these equations are also technically “balanced,” but on a test ONLY the lowest numbered choice, i.e., “4Y + 3R2 => 2Y2R3” would be correct. We ALWAYS want the equations with the lowest numbers.

Review:

You should now understand the basics for balancing chemical equations.

1. ALL balanced equations must obey the Law of Conservation of Mass, which means that they must have the same number of atoms of each kind on both sides of the equation.

2. The subscript tells how many atoms of each kind there are in a formula.

3. The coefficient is a multiplier, multiplies every atom in the formula along with its subscript, and is the ONLY number which may be changed in balancing equations.(Once formulas are correct, the ONLY way to add atoms is by adding groups.)